Dynkin diagrams of rank 20 on supersingular K3 surfaces

TL;DR

This paper classifies certain supersingular K3 surfaces with specific singularity configurations in odd prime characteristics, expanding understanding of their geometric and algebraic properties.

Contribution

It provides a classification of normal supersingular K3 surfaces with Milnor number 20 under particular prime characteristic conditions.

Findings

Classification of supersingular K3 surfaces with Milnor number 20

Identification of conditions on prime characteristic p

Analysis of Dynkin diagrams associated with singularities

Abstract

We classify normal supersingular K3 surfaces Y with total Milnor number 20 in characteristic p, where p is an odd prime that does not divide the discriminant of the Dynkin type of the rational double points on Y.